An application of the Helpman (1998) model to

the Oresund-region

Kristian MangorJonkoping International Business School, Sweden

Tutors:M. Andersson, M.Backman and

V. Jienwatcharamongkhol.

August, 2011

Abstract

This paper investigates the effect of the reduction of transport costOresundsbron has caused between the two subregions of the Oresund-region. The paper utilizes the the Helpman (1998) model and the pro-cedure used by Hanson (2005) for estimating this equation. The paperbrings a clear inside into the method and thus provides an excellent start-ing position, with evaluation of possible pitfalls.

Contents

1 Introduction 2

2 Background 4

3 Models and the derivation of the final equation 6

4 Data and method 12

5 Results 14

6 Conclusion 15

A OxMetrics 6.2 code used to estimate 19

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1 Introduction

An empirical test of the Helpman (1998) model is presented in this paperwith the testing ground being the Oresund-region in Scandinavia. This areahas been divided by a strait up until June 2000, where Oresundsbron was com-pleted. Thus an ex-ante and ex-post application of the Helpman (1998) modelwould yield interesting results in regards to the effect of a reduction in trans-port cost that the bridge has caused between the two sub-regions. The Helpman(1998) model is part of the economic sub-disciplin called New Economic Geog-raphy, which is gaining more and more ground and recognition. This shouldshould not come as an surprise since it incorporates the fact that the world isnot a homogeneous, flat plain. Unlike e.g. Neoclassical Trade Theory, wheretrade is a product of comparative advantage, new economic geography producestrade flows due to a love-for-variety effect first introduced by Dixit & Stiglitz(1977) and later utilized by Paul Krugman in his paper from 1979, which isa very powerful simplification that allows for monopolistic competition withmany firms. Furthermore, models based on comparative advantage (such as

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Ricardo’s, Heckscher-Ohlin model) assumes no transport cost in an attempt tosimplify the models. This is arguably both a strong assumption, but also a nec-essary pre-computer assumption so that the model could be solved analyticallyand thus possible to evaluate. Today, in the computer era, an analytical solu-tion is neat, but not necessary, and with the rediscovery (and mathemathicaladditions) of iceberg cost by Paul Samuelson in 1954 of von Thunen’s ’graineating ox’, transport cost can now be handled rather simple (Samuelson 1983)and the non-linear equation can be calculated.

By the use of the Helpman (1998) model and its equality conditions, this paperlooks into the effect of a sudden, but expected, change in transport cost betweentwo sub-regions in the Oresund-region in Scandinavia due to the completion ofthe Oresund bridge in July 2000, thus attempting to add further empiricalresearch of the Helpman (1998) model. The paper will in total estimate twoequations - one before and one after the completion of the bridge. The twoequations will be estimated and compared. The reason for using data starting3,5 year after the completion of the bridge is to let the population and businessenvironment adapt to the new situation, since it was found that the initialeffect of the bridge was less than expected (Matthiessen 2004). In the periodinvestigated, the region have had steady economic development without anyshocks of significance, except for the completion of Oresundsbron. Thus it willbe possible to investigate the effect in somewhat isolated circumstances, whichideally would provide new insights into the application of the Helpman (1998)model.

The empirical arena, the Oresund-region The Oresund-region consistsof Skane in southern Sweden and eastern Denmark including Zealand, Lolland-Falster, Mon and Bornholm. Of large cities it includes the Danish capital,Copenhagen, and Swedens third largest city, Malmo. A total of 3.732.000 peoplelive in the region (January 2010) of which two-thirds live in the Danish partand the rest in the Swedish part of the region. It is possible to travel withoutpassport between the Scandinavian countries and education and health care isfree for all citizens in all the Scandinavian countries, no matter which of thesecountries they come from. Furthermore, the language are, though different,quite alike and it is of no greater difficulty for a Danish person to understand aSwedish person, or vice versa. The Oresund-region has always been divided bya strait and it was only possible to cross by boat or airplane up until July 2000.This natural barrier combined with the small differences of the two sub-regions,has allowed each sub-region to create it’s own agglomeration and not make acomplete agglomeration together. That the opening of the bridge has had someeffect is evident from the increased traffic over the strait. Throughout the 1990’saround 2 million vehicles passed the strait per year. In the first couple of yearsafter the opening of the bridge, traffic didn’t match the expectations. In 2010,though, the vehicle traffic had increased to around 9 million per year (Oresund2010). The above map is of the Oresund-region.

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Structure The paper is structured with background in section 2. In section 3the background models are presented and the equation for estimation is derived.In section 4 the data used and the methodology are discussed and in section 5the results are presented. Section 6 brings the conclusion.

2 Background

Agglomeration and Transport cost This paper focuses on the effect ofchange in transport costs, which is shown by Krugman (1991) (among others)to affect the degree of agglomeration. If there was no transport cost, there wouldbe no agglomeration since everything (products, ideas, knowledge) could andwould be transported at zero cost and thus no justification for difference in rent.The different forces that cause agglomeration are named centripetal forces, andforces which cause dispersion are called centrifugal forces. In the review articleof Krugman (1998) six of these forces are discussed (three in each category):

Centripetal forces

• Market-size effects

• Thick labour markets

• Pure external economies

Centrifugal forces

• Immobile factors

• Land rents

• Pure external diseconomies

The market-size effects are the benefits of a large market, such as how easy itis to find a local supplier or a distributor. Thick labour markets refer to theincreased possibility of a good match between firm and employee, thusincreasing synergy effects. Pure external economies refer to positive spill oversthat agglomeration causes. This includes the concept of ideas, which is anon-rivalrous good, but also the increased local demand for intermediategoods. Of the centrifugal forces, immobile factors include natural resourcesand land. Land rents are obvious, but are also strongly related to immobilefactors. A typical example of pure external diseconomies is congestion, whichis a problem seen in almost every mayor city in the world. Congestion isactually a kind of transport cost, but normally the literature refers totransport costs as the cost of transporting between agglomerated areas andnot within the different agglomerated areas. Paul A. Samuelson revolutionizedtransport costs in 1954 by introducing the ”iceberg” kind of transport cost,even though it was introduced by von Thunen (1826) who noted that theoxen, who moves the grain, must eat some of it to move it one mile(Samuelson 1983). This was later on formalized in Samuelson (1954). Beforeits formalization, the most preferred technique to treat transport costs wereeither to ignore it or to create an entire market for transport costs, which

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made models unnecessarily complicated. With iceberg cost a certain part ofthe traded goods simply disappear - i.e. when sending y products to a tradingpartner, only y-x arrives (with 0 < x < y). In the extreme cases where x=0and x=y there is respectively no transport cost and no trade possible.

Market Potential The market potential is the total potential of a givenmarket based on itself and its surrounding markets demand, but negativerelated to the distance or cost of transport to these surrounding markets. Thiswas first captured in the market potential function of Harris (1954). Marketpotential is defined as the sum of demand by all n locations, each divided bytheir respective distance to the i’th location:

MP i ≡n∑j=1

(Mi

Dij

)(1)

, where MPi is the market potential in region i, Mi is demand by region j forgoods from region i, and Dij is the distance between regions i and j. Themarket potential of region i thus depends postively on demand from the otherregions, but negatively on distance. The market potential of a ’far away’region in this context thus approaches zero.

Market Access Market access is directly related to market potential and isof crucial importance. However, market access is only build into the modelswith the distance parameter, Dij . This parameter is important, but it doesnot capture everything. This paper will, however, only use the distanceparameter to capture transport cost due to the difficulty of measure othervariables and to keep consistency with the models, which is discussed later.The Oresund-region is a border region and transactions across borders aremore difficult than in a streamlined region (i.e. a national region), while thesedifferences also can produce transactions of different kind (Schack 1999).Besides the physical transaction cost, other costs could be languagedifferences, law differences and cultural differences. All these are important,but in the Oresund-region the differences are minor. The two languages,Swedish and Danish, are very similar and the cultures are alike, with anunderstanding of the differences. In regards to the law difference there isobvious great differences, but much has been done in the recent years tostreamline important laws, such as tax laws (Matthiessen 2004). However, thecost for crossing the bridge has been found to be a great obstacle for furtherintegration and thus agglomeration in the region (OECD 2003). For the sakeof simplicity, this paper will only include the distance parameter. The modelwhich the estimation equations are build upon are that of the Helpman (1998)extension of the Krugman model.

Reference paper In the Hanson (2005) paper a similar equation andapproach is utilized. Other papers, such as e.g. Redding & Venables 2004,

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Head & Mayer 2006, uses a different approach with bilateral trade data. Thathowever is not possible in this context, which is one of the main reasons thatthe Helpman (1998) model has been chosen. Another reason for that is to havean actual model to back up the estimation equation. A quick summary of theHanson (2005) paper follows here as to use later for reference.

In Hanson (2005) the data is based on 3075 counties in the United Statesfrom 1970 to 1990. To begin with, a simple market-potential function isestimated, based on Harris (1954). This function is then expanded to anaugmented market-potential function, similar to the one in this thesis. Hanson(2005) estimates with non-linear least squares and GMM and all estimationsyields plausible and exact results. It is found that distance does affectnegatively and that a larger housing sector, higher wages and higher personalincome all affect a region positively. The augmented market potential equationis found to have higher explanatory power than the simple market potentialfunction, although relative low. By using the equilibrium conditions from theHelpman (1998) model, Hanson finds that σ, µ and τ all have plausible results.Hanson also estimates these parameters using the more strict Krugman (1991)model and finds that σ and τ are consistent, but that the estimates of µ aretoo large.

3 Models and the derivation of the finalequation

The Krugman model New Economic Geography has it origin in the paperof Krugman (1979). The paper introduced a one factor model which differedfrom other existing theories of trade by having internal economies of scale asthe driving force. With the assumption of free entry and exit this allows formonopolistic competition with firm i having the basic production functionli = α+ βxi with (α, β > 0). Each firm does therefore only produce oneproduct. The consumers are assumed to prefer all products equally much,which is an approach borrowed from Dixit and Stiglitz (1977) work onmonopolistic competition. The utility function is U =

∑ni=1 τ(ci) , with ci

being the consumption of the i’th good. The function τ(ci) is assumed to beconcave with a global maximum, thus allowing an optimum consumption(excluding infinite consumption of good i). In equilibrium the model has anoptimum number of firms, each earning zero profit and a maximum amount ofutility. Krugman showed that technology difference or difference in factorendowments are not needed to provide initiatives for trade - the only thingthat is needed is love for variety. However, Krugman (1979) does notincorporate transport costs in any real way, since this would create fullagglomeration in one region due to the factor endowment, labour, is perfectlymobile. This was changed in his paper from 1980.

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In Krugman (1980) basically the same model is used1, but the paperinvestigates the effect of transport costs more thoroughly. These are of thebefore mentioned iceberg type. When trade opens and there is no transportcost, the only change that occurs is an increase in total utility due to thelarger variety of products, as inhabitants will divide their expenditure onproducts from home and abroad - increasing their utility while real wage staysunchanged. The firm sizes are also unchanged since they are determined bythe amount produced of each product, which has the following equation:

xi =α

( pw − β)(2)

When transport cost is introduced, the only thing that changes is the relativewage rate between the two regions: The relative larger region ”A” in regardsto region ”B”, has the higher relative wage (called the home market effect).The paper ends with introducing a variant of the model by including twodifferent kinds of product groups which is demanded by two differentpopulation groups. This is done to prove the home market effect.

In Krugman (1991) a model is introduced with two sectors - amanufacturing sector and an agricultural sector. It builds upon the earlierwork, but with great modifications. An agricultural sector has been introducedto keep income in each region and so as to be used as numeraire. Theproduction function of the industrial sector is the same as in the previouspapers and the basics of the utility function for manufactured products arealso similar. Furthermore, the iceberg transportation cost is also applied. Inthis model, output per firm is fixed due to the increasing returns to scaleproduction and free entry and exit of firms. The model thus describes theeffect of transport costs upon agglomeration and what other underlying factorsthat might influence it. There is no real dynamics in the model, but it yieldssome end results given different transport costs, which is the outcome of themodel: For high transport cost (and other parameters stable at a specificvalue) the outcome of the model is that manufacturing workers are dividedbetween the two regions in an equal way to agriculture. When transport costsare low, we have agglomeration of manufacturing workers in one region.

The model utilizes the Dixit & Stiglitz (1977) method of modelingmonopolistic competition. The utility curve is a basic function, where utilityof the two products (manufacturers and agricualtural products) each yieldssome utility, given the value of µ :

U = CµMC1−µA (3)

, which is a shared utility function for the total population of the economy.The total consumption of manufacturers are determined with the following

1The utility function U =∑ni=1 τ(ci) is replaced by U =

∑ni=1 c

θi ) with 0 < θ < 1, which

basically produce the same result.

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Figure 1: Marginal utility falls with increased consumption of one product.

equation, where N is the number of potential products and is assumed to belarge:

CM =

(N∑i=1

c(ε−1)/εi

)ε/(ε−1)

(4)

, with ε > 1. This secures that all products are consumed, since consumptionhas concave utility but the summing is linear (for illustration, see figure 1).The production of agricultural products is assumed to be linear and there isno transport cost connected to this sector (therefore good to use asnumeraire). The model assumes that population is one and that peasants(employees in the agricultural sector) is equal to (1− µ) divided equally toboth regions. Peasants are also assumed immobile. This ensures, as mentionedearlier, that all regions always have an income and thus meaning in the model.Employees in the second sector, manufacturers, are called workers and areassumed to be mobile. Their total number adds up to µ : µ = L1 + L2. Theproduction function in the manufacturing sector is assumed to be of increasingreturns to scale:

LMi = a+ bxi (5)

, where LMi is the amount of labour needed to produce x amount of product i.Since there is free entry and exit in the model, and given the utility curve,

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there will be zero profit. The transport cost is positive in this sector and issimplified to the inverse of the beforementioned iceberg kind, so that τ < 1.The price in region j, pj , is therefore equal to:

pj =

(ε

ε− 1

)βwj . (6)

Given the assumption of free entry and exit, the output per firm must be thesame in all regions, with the output function looking like this:

x1 = x2 =α(ε− 1)

β(7)

When estimating the market-potential function this paper will, as Hanson(2005), utilize much of the above model, but with the modification made byHelpman (1998). It is done since Hanson (2005) estimates equations based onboth models and finds the Helpman (1998) model to be more correct. Thusthe estimation procedure will utilize a lot of Krugman’s work, but with themodification made by Helpman (1998), where the agricultural sector isreplaced with a housing sector to improve the model.

The Helpman (1998) extension The housing sector in Helpman (1998) isintroduced as a non-tradable factor that works as a centrifugal force instead ofthe agricultural sector in Krugman (1991). People are assumed to freely beable to move between regions. It is also assumed that all activities of theperson is done in the region which it resides, i.e. all purchasing (manufacturers,housing) and working is done in the region of residence. The larger a region,the greater the variety of locally produced goods due to the same monopolisticcompetition framework used in Krugman (1991). This produces the twoopposing forces of the Helpman (1998) model. The centrifugal force is the costof housing. The larger the region compared to housing stock, the moreexpensive housing is. The centripetal force is the greater variety of goods. Theutility function of these two kind of goods is basically the same as Krugman(1991), but with housing replacing agricultural products.

With its foundation in the above theory, the following equilibrium equationswill be used. The equilibrium condition for the housing market:

PkHk = (1− δ)Yk (8)

, where Pk is the price of housing in region k and δ is the share of incomespent on manufacturers. The assumption that real wage will equalize betweenthe regions are also used:

Wr

(P 1−δr Iδr )

=Wk

(P 1−δk Iδk)

(9)

,where I, which is the price index, is measured by: I =∑Nj=1 pj .

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Furthermore, the consumers maximizes’ their utility of manufacturers subjectto the income constraint; the income spent on manufacturers δY :

CM =

(N∑i=1

x(ε−1)/εi

)ε/(ε−1)

(10)

st.δY =

N∑i=1

pixi

, which yields the first order condition (F.O.C.):(N∑i=1

xi(ε−1)/ε

)−1/(ε−1)

x1/εi − µpi = 0 (11)

And the second order condition (S.O.C.) verifies a maximum; S.O.C. < 0. Bytaking the ratio of F.O.C. for product i to the F.O.C. of product 1, we gainthe equation for the amount of product i, given price and quantity of product1: xi = p−εi pε1x1. Inserting this into the budget constraint and using thedefinition of the price index, the demand for product 1 is found:

x1 = p−ε1 Iε−1δY (12)

Product x1 is demanded in its own region and the surrounding regions, butthe demand from the surrounding regions are reduced by the transport cost.The general demand for product s can thus be stated as following:

xs = p−εs δ

(R∑r=1

YrIε−1r TDrs

)(13)

, where TDrs is equal to 1 when r = s.Given the free entry and exit of firms, profit is zero and supply is equal to

demand. Thus, replacing xs with α(ε−1)β , the following equilibrium equation is

obtained:

α(ε− 1)

β= p−εs δ

(R∑r=1

YrIε−1r TDrs

)(14)

To find the wage in one region the mark-up pricing rule (eq. 6) is used. Isolatefor p in eq. 6 and use this to replace p in eq. 14 such that:

α(ε− 1)

β=

(wβ

1− 1ε

)−ε

δ

(R∑r=1

YrIε−1r TDrs

)(15)

Solving for w we get:

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w =

(β

1−εε

ε−1ε

(δ

α(ε− 1)

)1/ε)(

R∑r=1

YrIε−1r TDrs

)1/ε

(16)

The first paranthese is normalized2 and the estimation equation is produced:

w =

(R∑r=1

YrIε−1r TDrs

)1/ε

(17)

The next step is to get rid of the price index and introduce the price of thehousing markets and the nominal wages for the R regions. This is done byfirst inserting the equilibrium condition for the housing market (eq. 8) into thereal wage equalization condition (eq. 9), where the right hand side is replacedby w3 and :

Wr(((1−δ)YrHr

)1−δIδr

) = w (18)

Isolating for Ir and inserting in the wage equation (10) so that the equationcan be estimated, the following is done:

Wj =

R∑Yr

Wr

w(

(1−δ)YrHr

)1−δ

ε−1δ

TDjr(1−ε)

1ε

(19)

Next step is to get all the variables with r as an index out:

Wj =

(R∑

(w)1−εδ (1− δ)

1−εδ +εY

1−εδ +ε

r Wε−1δ

r H(1−δ)(ε−1)

δr TDjr(1−ε)

) 1ε

(20)

and the rest are constants, so that:

Wj = C

(R∑Y

1−εδ +ε

r Wε−1δ

r H(1−δ)(ε−1)

δr TDjr(1−ε)

) 1ε

(21)

The constants are taken out of the paratese and then log is taken, which yieldsour augmented estimation equation:

log(Wj) = c+ ε−1log

(R∑Y

1−εδ +ε

r Wε−1δ

r H(1−δ)(ε−1)

δr TDjr(1−ε)

)(22)

2See Brakman et al. page 118.3To simplify the derivation.

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, which will be estimated in the reduced form of equation (23) - see below.With equation (23), the α parameters can be estimated and then solved in alinear system to uptain the values for µ, ε and τ . This is done to check if theparameters show plausible values. The term e is used instead of T to have anactual value. It will yield qualitively the same, since distance cannot benegative and zero distance also makes e = 1.

Summation In the above text the models has been outlined, the equationfor estimation as been derived, the area in context has been described andsupporting theory presented. The final estimation equation, which tests thehypothesis, is based on these models.

Hypothesis ”Has Oresundsbron, in the settings of the Helpman (1998)model, increased the wages and thus the market potential in theOresund-region, Scandinavia?”

To support the hypothesis the estimated parameters in the estimationequation:

log(Wj) = α0 + α1log

(R∑Y α2r Wα3

r Hα4r eDjrα5

)(23)

should have the following attributes: α1 is expected to be between 0 and 1, α2

is unknown, α3 is expected to be positive, α4 is expected to be positive andthe distance parameter α5 is expected to be negative.

4 Data and method

The parameters Distance is measured by travel time. This way ofcapturing distance is superior to that of concentric distance bands as Hanson(2005) uses because it takes differences in roads and natural barriers intoaccount. In regards to time versus kilometers traveled, the differences must besuspected to be minor. Furthermore, the assumption that people choose thequickest route instead of the shortest seems plausible.The times are calculated from the economic center (largest city) in each regionto the economic center of another region. Google Maps have been used tocalculate all time distances. In regards to travel time between Denmark andSweden, the time from each region to where the bridge begins (on either side)has been calculated and either 60 or 10 minutes have been added for the datarespectively before and after the bridge4. Furthermore, travel between thenorthern parts of both the Danish and Swedish part of the Oresund-region hasbeen assumed to be done by ferry between Helsingor and Helsingborg instead,

4Based on information from Matthiessen (2004).

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Table 1: Data presentation - all monetary terms are in DKK and distance inminutes.

Year 1999 Y W H DistanceMean value: 4925754455 212209 21003 99,95Median value: 2757500000 223086 13451 97Std. deviation: 9868789256 49002 33900 58,18Year 2004 Y W H DistanceMean value: 5716867469 242810 21370 78,07Median value: 3256000000 258807 13932 75Std. deviation: 11580175735 57450 33864 40,84

and with more regions doing this before than after the bridge. The travel timeassumed for this route is 30 minutes5.

Income (Y) is total income in a region. This varies substainally betweenregions. The wage variable (W) is the income variable divided by number ofemployed persons in a region. Housing stock is number of housing in a region.This could be either a small one-room apartment to a penthouse apartment ora villa. A better piece of data might have been total number of housing squaremeters in a given region. However, that data was not available. Furthermore,in the basic setting of this model it could be assumed that a place to sleep andeat is all an employee needs besides work. This might be seen as a strongassumption, but then again - if the model should include preferences forhousing it would quickly become extremely complicated, since some peoplewould like to live near water, others in the center of a city, others again insmall house or large house and so forth. The Danish and Swedish housing dataset are gathered respectively from Danmarks Statistik and StatistiskaCentralbyran.

Estimation The estimation procedure is in principle simple: Minimize theerrors while iterating on the 78 equations (due to the 78 regions) until thelowest possible residuals occur of the following equation:

log(Wj) = α0 + α1log

(R∑Y α2r Wα3

r Hα4r eDjrα5

)+ σ (24)

, with σ being the error term to minimize. This is, of course, done with theparameters being the same for all 78 equations and starting values are given(otherwise we would most likely see a non-optimal solution). The startingvalues were chosen based on the estimated values from the results fromHanson (2005), but with modifications along the way to improve the

5The ferry trip is just over 20 minutes and there is 4 connections per hour in daytime(thus average waiting time 7,5 minute in daytime). For interested, their currect homepage is:http://www.scandlines.com/en.

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estimation. For example, it was found that the initial values for the distanceparameter had to be positive in order to force the minimization process to findthe optimal value (otherwise it would stick to the given initial value, no matterits size). The program for estimation was made in OxMetrics 6.2 andconsisted basically of two loops, one outer for each equation and one inner forthe summation of the products. The estimation was in other words done withprogramming the actual way the calculations would have taken place (seeAppendix A for the code). The errors were tested in EViews 7 with a simpleJarque-Bera test to measure their normality.

(Dis)advantages As apparently most statistical software packages cannotcompute the above equation themselves and programming therefore is needed,the initial work is relative larger. Furthermore, easily used tests in moststatistical softwage packages are not easily applied here unless they are alreadyprogrammed. Of this reason, I have chosen to add the OxMetrics 6.2 code inthe appendix, so that other people who wish to continue the work in thisempirical arena has a better starting position.In the context of the chosen model (Helpman 1998), there is severaladvantages. First of, the model of Helpman (1998) supplies the possibility toimprove on something concrete. The Helpman (1998) model is thus a skeletonto change, add-on and improve. This is unlike unformulated models, wherethere is no center for the research. Secondly, the Helpman (1998) modelexhibit the general patterns that are seen and it connects the variables in use.Non-model based equations which includes variables that seems likely to affectmight be very good, but they demand a large amount of testing to be sure theexplanational power is correct or close to. The Helpman (1998) model allowsfor extra testing, since the basic parameters of ε, τ and ε can be found andevaluated if need be. An advantage which should be used if good results areobtained.

5 Results

The results can be seen in Table 2, with the standard errors in parentheses.For ease of reference the parameters will be restated: α0 is the constant, α1 isthe inverse degree of substitution, α2 is the power of the income variable, α3 isthe power of the wage variable, α4 is the power of the housing variable and α5

is the distance parameter. Their expected intervals are also shown. As can beseen the distance parameter (α5) is indeed negative as expected, which isconsistent with the theory and earlier findings. Compared to Hanson (2005)the distance parameter is ’less’ negative (lower in absolute value). This mightbe due to a smaller area. In regards to the other parameters (disregarding theconstant) all change signs from 1999 to 2004 and all are insignificant, which isproblematic. The reason for that is that the parameter values for the year1999 stays within its expected values, while that they do not for 2004.The distance parameter is insignificant, but here it must be noted that the

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Table 2: The estimated values.α0 α1 α2 α3 α4 α5

Variable: Constant ε−1 Y W H DistanceExp. Value: - ]0; 1[ 6= 0 > 0 > 0 < 0Year 1999 0.057196 0.17352 -0.73146 6.6084 0.53949 -1.4992(std. error) (0.41542) (0.89134) (3.7587) (33.946) (2.7733) (36.293)Year 2004 0.43390 -0.63302 0.12703 -1.6990 -0.062791 -1.7832(std. error) (0.34775) (9.1306) (1.8330) (24.507) (0.90664) (61.737)

Figure 2: Errors’s distribution for year 1999

non-linear estimation procedure yielded ’no convergence’ when the initial valuewas too large (and positive). When α5 was a low, but positive value, itconverged to a negative value with ’strong convergence’ (below 8,500iterations). Thus it must be extracted that in the given context, the distanceparameter must be negative.

The residuals were tested in EViews 7 and for both years the Jarque-Beratest could not reject normality (see figure 2 and 3). As can be seen in the twofigures, the Jarque-Bera tests yields a certainty above 0.05. Both have meanswhich essentially is zero, as it should be. Both error-sets shows a larger degreeof negative extreme values than positive, but within acceptable limits. Thus,the estimation procedure produced valid errors.

6 Conclusion

That the results are insignificant and in general inconsistent reduces thequality of the results of this study. The problem of insignificance can only behandled with a larger population, something that was never possible in thisstudy due to its context. Furthermore, it does not change that the estimatesare the most likely estimates based on the sample size. However, that the

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Figure 3: Errors’s distribution for year 2004

estimates in general are inconsistent is a problem: α1, α2, α3 and α4 allchange signs from one year to another, from being within the expected valuesin 1999 to being outside the expected values in 2004.

The α5 parameter, which is the weight of transport cost, is consistenlynegative and thus support the theory that transport cost negatively affects thewage in a region. However, it is also insignificant and it increases in absolutevalue - not decreases - as predicted by the theory. Thus the completion of thebridge has affected the market potential and wages negatively, which rejectsmy hypothesis. This rejection, though, is based on insignificant results. Thebest possible explanation for the rejection (beside that the sample being toosmall, yielding insignificant results) is that only a few regions have hadincreased wages while most have been affected less positive from the buildingof the bridge.As an end remark it should be noted that all iterations of the data set yieldednegative α5 and that no positive value of α5 appaered with a respons of ’goodconvergence’ (thus all these had ’no convergence’). Here, this paper finds asmall pocket of support for the theory that transport costs affects negatively,while there is no evidence opposing the theory.

As such, the results themselves is of minor use in the scientific world andthis paper greatest contribution to that is the ready set application of theHelpman (1998) model. Furthermore, it does support the theory in thattransport cost affects negatively and shows that the Helpman (1998) is ofminor use in measuring a single transport improving project and should beused for larger areas. Also, this paper barks the notion and transport costshould be measured in time distance instead of concentric distance bands orother rough estimation methods. Time distance is what matters to people, notif they are within e.g. a 100 kilometer in bird flight.

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Further research This paper gives a starting position to expand theempirical testing ground for the Helpman (1998) model, which isrecommended so the model can be improved and increasingly validated.Further research should apply a larger sample to insure statistical significantresults. The Hanson (2005) paper had significant results by including 3075counties, while this paper had insignificant results with 78 regions.Furtermore, the future research is encourage to use time distance instead ofe.g. concentric distance bands - especially if they work in e.g. mountainousareas or others which would create significant different travel time comparedto the flight distance. And lastly, the code below is to free use and editing.

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References

[1] Brakman, S., Garretsen, H. van Marrewijk, C. (2009), An introduction togeographical economics, Cambridge University Press.

[2] Dixit, A. K. and Stiglitz, J. E. (1977), Monopolistic Competition andOptimum Product Diversity, The American Economic Review, vol. 67, no.3 (June 1977).

[3] Hanson, G. H. (2005), Market potential, increasing returns and geographicconcentration, Journal of International Economics, 67, 1-24.

[4] Harris, C. D. (1954), The market as a factor in the localization ofproduction, Annals of the Association of American Geographers, 1954, vol.44, no. 4 (Dec. 1954), pp. 291-391.

[5] Helpman, E. (1998), The Size of Regions,http://www.google.com/books?hl=dalr=id=4M1r3OKaYj4Coi=fndpg=PA33dq=Help-man+1998ots=wXUJcAR6aTsig=A8Rx4bVuGvcquzH7dGdbpnkixNQv=onepageqf=false

[6] Krugman, P. (1979), Increasing Returns, Monopolistic Competition andInternational Trade, Journal of International Economics, vol. 9, 469-479.

[7] Krugman, P. (1980), Scale Economics, Product Differenttiation, and thePattern of Trade, The American Economic Review, vol. 70, no. 5 (Dec.1980), pp. 950-959.

[8] Krugman, P. (1991), Increasing Returns and Economic Geography, Journalof Political Economy, vol. 99, no. 9.

[9] Krugman, P. (1998), What’s new about the New Economic Geography?,Oxford Review of Economic Policy, vol. 14, no. 2.

[10] Matthiessen, C. W. (2004), The resund Area: Pre- and post-bridgecross-border functional integration: the bi-national regional question,GeoJournal, vol. 61, no. 1, pp. 31-39.

[11] OECD (2003), OECD Territorial Reviews, resund, Denmark/Sweden,www.oecd.org.

[12] Oresund, Infofolder (2010), 10 ar, Øresundsbron og Regionen,www.oresundsbron.com.

[13] Samuelson, P. A. (1954), The Transfer Problem and Transport Costs, II:Analysis of Effects of Trade Impediments, The Economic Journal, vol. 64,no. 254 (June 1954), pp. 264-289.

[14] Samuelson, P. A. (1983), Thunen at Two Hundred, Journal of EconomicLiterature, vol. 21, no. 4 (Dec. 1983), pp. 1468-1488.

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[15] Schack, M. (1999), On the Multi-Contextual Character of Border Regions,39th Congress of the Regional Science Association, 23-27 August 1999 inDublin.

A OxMetrics 6.2 code used to estimate

#include <oxstd.h>

#include <oxfloat.h>

#import <maximize>

static decl s_vY, s_mX, s_iEval = 0, vEps;

Initialize(const mDat, const avY, const amX, const avP)

{

decl iN, iK;

iN = rows(mDat);

iK = columns(mDat);

avY[0] = mDat[][1];

amX[0] = mDat[][5:8];

avP[0] = < 0.1 ; 2.14980 ; -0.053677 ; 0.1795 ; 0.26530 ; 2.000>;

println("\rInitial parameter values

are: \r", "%r", {"a0", "a1", "a2", "a3", "a4", "a5"}, avP[0]);

}

AvgLnLiklRegr(const vP, const adLnPdf, const avScore, const amHess)

{

decl vLnL, iN, dAlpha, vBeta, dA0, dA1, dA2, dA3, dA4, dA5,

vw, vY, vW, vH, vD, j, k, dC, dKLoop;

dA0 = vP[0];

dA1 = vP[1];

dA2 = vP[2];

dA3 = vP[3];

dA4 = vP[4];

dA5 = vP[5];

dC = 0;

dKLoop = 0;

iN = 78;

vw = s_vY;

vY = s_mX[][2];

vW = s_mX[][1];

vH = s_mX[][0];

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vD = s_mX[][3];

vEps = constant(.NaN,iN,1);

for(j = 0; j<iN; j++)

{

dKLoop = 0;

for(k = 0; k < iN; k++)

{

dKLoop = dKLoop + (vY[k].^dA2 .* vW[k].^dA3 .*

vH[k].^dA4 .* exp(vD[dC] .*dA5 ));

dC = dC + 1;

}

vEps[j] = log(vw[j*(iN-1)]) - (dA0 + dA1*log(dKLoop));

}

adLnPdf[0] = -vEps’*vEps;

s_iEval = s_iEval + 1;

return !ismissing(adLnPdf[0]);

}

Estimate(const avP, const adLnPdf)

{

decl vS, ir;

ir = MaxBFGS(AvgLnLiklRegr, avP, adLnPdf, 0, 1);

return ir;

}

Output(const ir, const vP, const dLnPdf)

{

decl mHess, mS2, dSigma, dStdError;

println("\rThe number of calls of the log likelihood function = ", s_iEval);

println("MaxBFGS returns ’", ir, "’ meaning ’", MaxConvergenceMsg(ir),"’.");

Num2Derivative(AvgLnLiklRegr, vP, &mHess);

mS2 = invert(mHess*mHess’)/(rows(vEps));

dSigma = (1/rows(vEps))*vEps’*vEps;

mS2 = dSigma*mS2;

dStdError = sqrt(diagonal(mS2));

println("\rOptimal parameter values are: \r", "%r", {"a0", "a1",

"a2", "a3", "a4", "a5"}, "%c", {"Estimates", "Std Error"}, vP~dStdError’);

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println("The epsilon vector equals in this case: \r", vEps);

println(mHess);

}

main()

{

decl mDat, vP, ir, dLnPdf, avScore, amHess, iK, vPTr;

mDat = loadmat("C:\\Documents and Settings\\...\\File.xls");

Initialize(mDat, &s_vY, &s_mX, &vP);

ir = Estimate(&vP, &dLnPdf);

Output(ir,vP,dLnPdf);

}

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